Design and Analysis of a Multi-Input Multi-Output System for High Power Based on Improved Magnetic Coupling Structure

Abstract

Conventional inductive contactless power transfer (ICPT) systems have only one energy transmission path, which makes it challenging to meet the power transmission requirements of high-power and reliability. This study proposes a novel multiple-input multiple-output (MIMO) ICPT system. The three-dimensional finite element analysis tool COMSOL is utilised to study various magnetic coupling structures, analyse the influence of cross-coupling between coils on the same side, design the circuit based on this, propose a parameter configuration method for resonance compensation, and, finally, build an experimental platform with small magnetic coupling structures for single-input single-output systems (SISO) and MIMO systems. The results indicate that the co-directional connection of the coils of the E-shaped and UE-shaped magnetic coupling structures has a strengthening effect on the secondary side coupling. The magnetic coupling structure of the E-shaped iron core exhibits the best transmission performance. The transmission power of the MIMO system with the E-shaped magnetic coupling structure as the core device is significantly improved. In addition, the output power is unchanged after a secondary side fault, which verifies the accuracy of the proposed method.

1. Introduction

Contact slip rings are widely utilised as a conventional energy transmission method, but contact and friction cause wear during long-term operation. Therefore, several control systems for automatic machines require wireless transmission of power. Owing to its robustness and high reliability [1], ICPT technology has been widely utilised in high-power equipment, such as medical CT, trains, electric vehicles, mines, aerospace [2,3,4,5], as well as in low-power equipment, i.e., power devices, such as implantable devices and consumer electronics [6,7].

The main challenge faced by ICPT technology is its low transmission efficiency and output power. The most immediate cause of this challenge is that the leakage flux in the ICPT system requires a magneto resistive path through a large air-gap, resulting in weak coupling [8]. The leakage inductance is reduced by designing a winding arrangement to improve the coupling coefficient [9]. The structure of U, E cores are improved based on the non-contact system, and the coupling coefficient is improved within the existing physical size range [10]. Based on zero-voltage switching, full-bridge rectifier inverter and DC–DC converter, the effect of the air-gap on the system during rotation was tested [11].

To improve the stability and reliability of the ICPT system output, the decoupling and symmetrical design of the coils are used to ensure the long-term stable and reliable operation of the satellite system [12]. By comparing different compensation topologies, it is determined that when the coil has displacement deviation, the rated power can be output by adopting a reasonable compensation method [13]. The ICPT polyphase system is proposed to be distributed in an orthogonal manner to capture the magnetic field in any vertical and horizontal directions [14], which significantly improves the reliability and output power of the system. A multivariable control strategy is proposed, which uses the optimal combination of all control variables to maximize the efficiency of IPT systems when regulating power and even under large coil misalignments and load variations [15]. The effects of different circuit compensation methods on the output power are studied [16,17,18]. A comprehensive investigation into the use of multi-coil receiver set to improve the misalignment tolerance has been presented, which is suitable for charging applications in low-power planar wireless charging pad systems and high-power electric-vehicles, such as modern trams, automatic guided vehicles, and passenger cars [19]. According to a predetermined misalignment tolerant range, a method has been proposed which can limit the fluctuation of the output current within a certain range and maintain the ZPA input condition [20].

For multi-coil wireless transmission systems, a decoupling transformer is adopted to eliminate the influence of ipsilateral coupling [21]. The desired control system can quickly adjust the output voltage of the secondary side to the design value. The influence of coupling between multiple coils at a close distance is discussed, and a high-power ICPT system with double primary edges is constructed [22]. Additionally, the characteristics of coupling coils with different shapes has been studied, including the transmission characteristics of coils, the relationship between coil size and coupling coefficient [23]. In [24], the power is transmitted wirelessly to a single secondary coil through multiple strongly coupled coils, and it is concluded that the transmitted power will increase with transmitting coils. A parallel power supply topology for ICPT systems is proposed [25], which can achieve high-power output economically, efficiently, and reliably. In addition, a control strategy has been developed to maximize energy efficiency under various misalignment conditions and upgrade the WPT system’s power capacity with low-power and low-cost semiconductors [26]. In [27], the review is concluded with the discussion of several fundamental challenges and prospects of high-power wireless power transfer systems.

Research on high-power output is applied mainly to wireless railcars, and the displacement deviation generated by the coupled coil during dynamic wireless power transfer is likely to cause power fluctuations [28]. In contrast, the magnetic coupling structure of the wireless transmission system in the medical CT and aerospace fields is always in a state of no displacement deviation between the primary and secondary coils during use. However, it is often necessary to keep the shape unchanged owing to the physical space constraints. Under a specific size, the power transmission capability of the ICPT system is improved, and the transmission efficiency requirements are met. This type of ICPT system that does not require relative displacement requires high power, high-efficiency transmission, and high reliability, and requires further research.

For the high-power output system (100 kW and above) with no relative displacement between the primary and secondary sides of the coupling system during operation and high-reliability requirements, in this paper, a multi-coil magnetic coupling structure is proposed. Firstly, the magnetic circuit of single-coil and multi-coil is analysed. The influence of mutual inductance between coils on the magnetic coupling is studied, the circuit of the MIMO system is designed, and the method of resonance parameter configuration is proposed. Finite element simulation software COMSOL was used to simulate the proposed magnetic coupling structure’s transmission power, efficiency, and output coil faults. Finally, a small experimental device of the SISO and MIMO systems is built to verify the correctness of the proposed method.

2. Analysis of Magnetic Coupling Structure

2.1. Magnetic Coupling Structure of Single-Coil and Multi-Coil

The high-power wireless power transmission system of medical CT has precise requirements for the size of the magnetic coupling structure; hence, it is necessary to improve the transmission capacity of the coupling system under the specified size. The magnetic coupling structure is the core of the ICPT system. Figure 1 illustrates a sectional view of the three shapes of iron cores cut along the centre. They are U-shaped, E-shaped, and UE-shaped magnetic coupling structures. The differences between the three structures are indicated by the red circles. The core, coil, and air-gaps are illustrated in Figure 1a. The lower and upper iron cores which are entirely symmetrical along the air-gap, are the primary and secondary side coils, respectively. To improve the power transmission capability of the coupling structure, this study proposes a multi-coil coupling structure, as illustrated in Figure 1b,c. For convenience of analysis, the magnetic coupling structure satisfies the following three conditions:

(1) The dimensions, that is, the inner diameter, outer diameter, height, and air-gap spacing are the same;

(2) The set of coil pairs are symmetrical along the air-gap. In Figure 1a–c, the ratio of the number of coil pairs formed by the primary side and the secondary side is 1:2:3;

(3) The total number of turns of the primary and secondary coils of the three structures illustrated in Figure 1a–c are the same. The ratio of turns of the coil pairs of the three structures is 3:2:1.

Among them, the coil connection mode of E-shaped and UE-shaped magnetic coupling structures is that the primary coil is connected in series in the same direction. Each secondary coil is regarded as the output end. After passing through the DC/DC converter and rectifier bridge, the output end is connected in parallel to supply power to the load.

2.2. Magnetic Circuit Analysis of Single-Coil and Multi-Coil Magnetic Coupling Structures

Assuming that the primary coils are all supplied with a 1 A current in the same direction, the three-dimensional finite element simulation software analyses the magnetic circuits of the three magnetic coupling structures of U-shape, E-shape, and UE-shape. Figure 2 illustrates the magnetic flux density distribution in the direction perpendicular to the magnetic coupling structure, and the arrows indicate the direction of the magnetic field lines. The right-hand side of the graph represents the magnetic flux density. The intensity is differentiated by the shade of the colour. Red indicates the maximum magnetic flux density, and blue indicates the minimum magnetic flux density. The three magnetic coupling structures adopted Alloy Powder Core Ferrite, with an inner diameter of 78.5 mm and outer diameter of 103.75 mm, the unilateral height of 21.5 mm, air-gap of 5 mm, and experimental frequency of 10 kHz. The value of the relative permeability is 4000, and the value of the electrical conductivity is 1 × 10⁻¹² S/m. The vertical toothed core width is the same in each magnetic coupling structure. The magnetic flux densities of the three structures at each height at an abscissa of 80 mm in Figure 2, are illustrated in Figure 3.

As illustrated in Figure 2 and Figure 3, under the same excitation, the multi-coil magnetic coupling structure can enhance the magnetic flux density in the primary and secondary iron cores, which further verifies that the E-shaped and UE-shaped magnetic coupling structures can be applied to high-power wireless power transmission systems.

2.3. Magnetic Field Analysis between Multiple Coils

Figure 4 illustrates the magnetic field generated when two coaxial coils pass currents in the same or opposite directions under the same magnetic field environment. The self-inductance and mutual inductance of the two coils are $L_1$, $L_2$, and $M$, respectively. Therefore:

$$\left\{\begin{array}{l}{\varphi }_1=L_1{I}_1\pm M{I}_2\\ {\varphi }_2=L_2{I}_2\pm M{I}_1\end{array}\right.,$$

(1)

Among them, $L_1$ and $L_2$ represent the self-inductance of the outer and inner coils, respectively. $I_1$ and $I_2$ are the injected currents of the two sets of coils, respectively, while ${\varphi }_1$ and ${\varphi }_2$ are the magnetic fluxes of the two sets of coils, respectively. When the two sets of coils pass into the same direction current, both equations of Equation (1) take ‘+’; when the two sets of coils pass into opposite currents, both equations of Equation (1) take ‘−’. It can be observed that in the model illustrated in Figure 4, when the two sets of coils are passed with the same direction current, the mutual inductance between the coils increases the magnetic flux. Furthermore, the larger the mutual inductance, the more pronounced the increasing effect, and vice versa when the reverse current is passed.

3. Design and Analysis of MIMO System Circuit

3.1. MIMO System Circuit

In this study, the number of inputs depends on the number of coil pairs in the magnetic coupling structure; hence, the U-shaped iron core constitutes the SISO system, and the E-shaped and UE-shaped cores constitute the MIMO system. A schematic diagram of the ICPT system is illustrated in Figure 5, with the magnetic coupling structure illustrated in Figure 1b as the core device. The two primary coils of the system are connected in series. $U_s$, $U_{s1}$, and $U_{s2}$ are the outputs of the high-frequency power supply and output voltage of the two secondary-side circuits. $C_p$, $C_{s1}$, and $C_{s2}$, are the compensation capacitances of the primary and two secondary coils. $R_p$, $R_{s1}$, $R_{s2}$ are the internal resistances of the primary and secondary coils, respectively. $I_p$, $I_{s1}$, $I_{s2}$ are the currents of the primary and secondary coils, respectively.$M_p$, $M_{p1s1}$, $M_{p1s2}$, $M_{p2s1}$, $M_{p2s2}$, and $M_s$ are the mutual inductances between the primary coils, primary coil and two secondary coils, and secondary coils, respectively. Because the primary and secondary sides are completely symmetrical structures, there is $M_p=M_s$, and $M_{p1s2}=M_{p2s1}$. $R_d$ is the load, $U_d$ is the DC voltage across the load. The output end of the secondary circuit is adjusted to the same DC voltage through the rectifier bridge and DC/DC converter. It is connected in parallel to supply power to the load. Accordingly, for the convenience of analysis, the equivalent circuit diagram of the MIMO system is illustrated in Figure 6, where $R_1$ and $R_2$ represent the equivalent loads, and $U_{s1}$ and $U_{s2}$ represent the voltages of the equivalent loads.

In Figure 6, three voltage equations for the primary and secondary loops are expressed in Equation (2).

$$\left\{\begin{array}{l}{\dot{U}}_S=j\omega M_{p1s1}{\dot{I}}_{s1}+j\omega M_{p1s2}{\dot{I}}_{s2}+j\omega (L_{p1}+M_p){\dot{I}}_p+j\omega M_{p2s1}{\dot{I}}_{s1}\\ \hspace{1em} +j\omega M_{p2s2}{\dot{I}}_{s2}+j\omega (L_{p2}+M_p){\dot{I}}_p+\frac{{\dot{I}}_p}{j\omega C_p}+{\dot{I}}_p{R}_p\\ \\ j\omega (M_{p1s1}+M_{p2s1}){\dot{I}}_P+j\omega M_s{\dot{I}}_{s2}+{\dot{I}}_{s1}(R_{s1}+j\omega L_{s1}+\frac{1}{j\omega C_{s1}})+{\dot{U}}_{s1}=0\\ j\omega (M_{p2s2}+M_{p1s2}){\dot{I}}_p+j\omega M_s{\dot{I}}_{s1}+{\dot{I}}_{s2}(R_{s2}+j\omega L_{s2}+\frac{1}{j\omega C_{s2}})+{\dot{U}}_{s2}=0\end{array}\right.$$

(2)

where $\omega$ denotes the operating angular velocity of the system.

3.2. Resonance Compensation Parameter Configuration Method

Because the compensation topology can improve the power transfer capability, minimise the reactive power rating of the power supply, and help achieve power soft switching in power electronic devices [19], it is an integral part of wireless transmission. Next, the configuration method of the compensation capacitors $C_p$, $C_{s1}$, and $C_{s2}$ in Figure 6 is proposed. Suppose k is the current ratio of the two secondary loops.

$$k=\frac{I_{S1}}{I_{S2}},$$

(3)

Then, the voltages of secondary site in Equation (2) can be changed to

$$\left\{\begin{array}{l}j\omega (M_{12}+M_{23}){\dot{I}}_P+{\dot{I}}_{s1}(R_1+j\omega L_{s1}+\frac{j\omega M_{24}}{k}+\frac{1}{j\omega C_{s1}})+{\dot{U}}_{s1}=0\\ j\omega (M_{34}+M_{14}){\dot{I}}_P+{\dot{I}}_{s2}(R_2+j\omega L_{s2}+jk\omega M_{24}+\frac{1}{j\omega C_{s2}})+{\dot{U}}_{s2}=0\end{array}\right.,$$

(4)

When the secondary side circuits are in the resonance state, the compensation parameters $C_{s1}$ and $C_{s2}$ satisfy Equation (5).

$$\left\{\begin{array}{l}\frac{1}{\omega C_{s1}}=\omega L_{s1}+\frac{\omega M_{24}}{k}\\ \frac{1}{\omega C_{s2}}=\omega L_{s2}+k\omega M_{24}\end{array}\right.,$$

(5)

Because the coil resistance is small and approximately ignored, $R_{s1}=R_{s2}\approx 0$, Equation (4) can be rewritten as Equation (6) assuming perfect compensation on the secondary site:

$$\begin{array}{l}j\omega M_{\mathrm{eq}1}{\dot{I}}_P+{\dot{U}}_{s1}=0\\ j\omega M_{eq2}{\dot{I}}_P+{\dot{U}}_{s2}=0\end{array}$$

(6)

where $M_{eq1}$ and $M_{eq2}$ are the equivalent mutual inductances of the secondary coil, respectively, and there are $M_{eq1}=M_{p1s1}+M_{p1s2}$ and $M_{eq2}=M_{p2s2}+M_{p2s1}$.

From Equation (6), it can be observed that in the resonance state, the ratio $n$ of the output voltage of the secondary-side circuit can be expressed as

$$n=\left|\frac{{\dot{U}}_{s1}}{{\dot{U}}_{s2}}\right|=\frac{M_{\mathrm{eq}1}}{M_{eq2}},$$

(7)

The relationship between the DC resistance after passing through the rectifier bridge and AC resistance before passing through the rectifier bridge is [29].

$$\left\{\begin{array}{l}{R}_{dc1}=\frac{{\pi }^2{R}_1}{8}\\ R_{dc2}=\frac{{\pi }^2{R}_2}{8}\end{array}\right.,$$

(8)

The relationship between the DC voltage after passing through the rectifier bridge and AC voltage before passing through the rectifier bridge is

$$\left\{\begin{array}{l}\left|{\dot{U}}_{dc1}\right|=\frac{\pi }{2\sqrt{2}}\left|{\dot{U}}_{S1}\right|\\ \left|{\dot{U}}_{dc2}\right|=\frac{\pi }{2\sqrt{2}}\left|{\dot{U}}_{S2}\right|\end{array}\right.,$$

(9)

After passing through the rectifier bridge and DC/DC converter, the relationship between the voltage and resistance is

$${\dot{U}}_L=\frac{\pi }{2\sqrt{2}}\left|{\dot{U}}_{s1}\right|=\frac{\pi }{2\sqrt{2}}n\left|{\dot{U}}_{s2}\right|,$$

(10)

$$2R_d=\frac{{\pi }^2}{8}{R}_1=\frac{{\pi }^2}{8}{n}^2{R}_2,$$

(11)

From Equations (10) and (11), it can be observed that the resistance relationship between the two circuits on the secondary side in Figure 6 is

$$\frac{R_1}{R_2}=n^2,$$

(12)

Therefore, there is $\left|\frac{{\dot{I}}_{s1}}{{\dot{I}}_{s2}}\right|=\left|\frac{{\dot{U}}_{s1}}{{\dot{U}}_{s2}}\right|/\frac{R_1}{R_2}=\frac{1}{n}$. Combined with Equation (3) that:

$$k=\frac{1}{n},$$

(13)

Substituting Equation (13) into Equation (5), the compensation capacitor configuration conditions for the two circuits on the secondary side to reach the resonant state are obtained as follows:

$$\left\{\begin{array}{l}\frac{1}{\omega C_{s1}}=\omega L_{s1}+n\omega M_{s1s2}\\ \frac{1}{\omega C_{s2}}=\omega L_{s2}+\frac{\omega M_{s1s2}}{n}\\ n=\frac{M_{\mathrm{eq}1}}{M_{eq2}}\end{array}\right.,$$

(14)

The total impedance of the two secondary circuits is represented by $Z_{s1}$ and $Z_{s2},$ respectively:

$$\begin{array}{l}{Z}_{s1}=R_1+R_{s1}+j\omega L_{s1}+\frac{1}{j\omega C_{s1}}\\ Z_{s2}=R_2+R_{s2}+j\omega L_{s2}+\frac{1}{j\omega C_{s2}}\end{array}$$

(15)

Then, the secondary side circuit current can be expressed as:

$$\begin{array}{l}{\dot{I}}_{s1}=\frac{j\omega M_{\mathrm{eq}1}{\dot{I}}_p}{Z_{s1}}\\ {\dot{I}}_{s2}=\frac{j\omega M_{eq2}{\dot{I}}_p}{Z_{s2}}\end{array}$$

(16)

Substituting Equation (16) into Equation (2), the impedances $Z_{r1}$ and $Z_{r2}$ of the secondary equivalent circuit reduced to the primary circuit are

$$\begin{array}{l}{Z}_{r1}=\frac{{\omega }^2{M}_{\mathrm{eq}1}{}^2}{Z_{s1}}\\ Z_{r2}=\frac{{\omega }^2{M}_{eq2}{}^2}{Z_{s2}}\end{array}$$

(17)

For the primary circuit to reach the resonance state, the configuration conditions that the primary-side compensation capacitor needs to meet are

$$\frac{1}{\omega C_P}=\omega (L_{P1}+L_{P2}+2M_p),$$

(18)

Therefore, in the equivalent circuit illustrated in Figure 6, when the compensation capacitors $C_p$, $C_{s1}$, and $C_{s2}$ of the primary and secondary circuits satisfy Equations (14) and (18), respectively, the MIMO system is in the resonant state.

4. Analysis of MIMO System Performance

Output power, transmission efficiency, and system operating performance after failure are essential indicators for evaluating system performance.

4.1. Analysis of Power and Efficiency Analysis

In the resonance state, the system output power is:

$$\begin{array}{cc}{P}_{out}& =\left|{\dot{U}}_{\mathrm{s}1}\right|\left|{\dot{I}}_{s1}\right|+\left|{\dot{U}}_{\mathrm{s}2}\right|\left|{\dot{I}}_{s2}\right|\hfill \\ & =\left|{\dot{I}}_p^2{Z}_{r1}\frac{R_1}{R_1+R_{s1}}\right|+\left|{\dot{I}}_p^2{Z}_{r2}\frac{R_2}{R_2+R_{s2}}\right|\end{array}$$

(19)

From Equations (12), (14), and (17), because $R_p$, $R_{s1}$, $R_{s2}$ are small, it is assumed in the following derivation: $Z_{r1}=Z_{r2}$ and $R_1/\left(R_1+R_{s1}\right)=R_2/\left(R_2+R_{s2}\right)$.

Equation (19) can be simplified as:

$$P_{out}=\mathrm{Re}\left(\frac{U_s^2}{2Z_{r1}}\right),$$

(20)

where Re (*) represents the real part of a complex number.

Similarly, the output power of the SISO system is:

$$P_{out\_U}=\mathrm{Re}\left(\frac{U_s^2}{Z_{r\_U}}\right),$$

(21)

where $Z_{r\_U}$ is the impedance of the SISO system from the secondary to primary side.

When using the multi-coil coupling structure, the $M_{eq1}$ and $M_{eq2}$ of the MIMO system decreases because the number of turns of each set of coils in the E-shaped magnetic coupling system is half that in the U-shaped magnetic coupling system; in addition, according to the equivalent circuit in Figure 6, the two output terminals supply power to the load in parallel; hence, $R_1=n^2{R}_2=2R_u$, where $R_u$ is the equivalent load of the U-shaped magnetic coupling structure. In the resonance state, Equation (17) can be simplified as:

$$Z_{r1}=\frac{{\omega }^2{M}_{\mathrm{eq}1}{}^2}{R_1+R_{s1}},$$

(22)

The MIMO system doubles the mutual inductance while reducing it. Therefore, $2Z_{r1}<Z_{r\_U}$. Thus, according to Equations (20) and (21), it can be observed that the MIMO system improves the output power.

The transmission efficiency of MIMO system is as follows:

$$\eta =\frac{P_{out}}{P_{in}}=1-\frac{R_p}{R_p+\frac{2{\omega }^2{M}_{eq1}{}^2}{\frac{R_s^2}{R_1}+R_1+2R_s}},$$

(23)

Nevertheless, at the same time, according to Equation (23), it can be observed that the decrease of $M_{eq1}$ and $M_{eq2}$ and the increase of $R_1$ will cause a decrease in transmission efficiency. Therefore, there is an optimal multi-coil magnetic coupling structure that significantly increases the transmission power of the MIMO system within the allowable range of reduced transmission efficiency.

4.2. Failure Analysis

An open circuit is a common fault of coils, especially wounds with thinner multi-strand enamelled wires. In addition to de-soldering, the reason for this failure is likely to be mildew after the coil is damp; therefore, the regular operation of the conventional SISO system is affected. In Figure 6, the circuit connected by $R_1$ is the secondary-side circuit 1, and the circuit connected by $R_2$ is the secondary-side circuit 2. Furthermore, consider the fault of the secondary-side circuit 1 coil as an example to analyse the reliability of the system operation.

Assuming that circuit 1 is disconnected, it can be observed from Figure 5 and Figure 6 that the two groups of power supplies will no longer power the load at this time, and the equivalent load $R_2$ will become 1/2 of the original. After circuit 1 is disconnected, the total impedance of circuit 2 is

$$△X=\omega L_{s2}-\frac{1}{\omega C_{s2}},$$

(24)

$$Z_2{}^{\prime }=R_{s2}+j△X+\frac{R_2}{2},$$

(25)

When ignoring the internal resistance loss of the coil, the output power is:

$$P_{out}=\mathrm{Re}\left(\frac{\left|U_s^2\right|(j△X+\frac{R_2}{2})}{{\omega }^2{M}_{eq2}^2}\right),$$

(26)

When ignoring the internal resistance loss of the coil, and the secondary side coil operates normally, the output power in the resonance state is:

$$P_{out}=\frac{\left|U_s^2\right|R_2}{2{\omega }^2{M}_{eq2}^2},$$

(27)

According to Equations (26) and (27), the output power of the system remains unchanged after the secondary side circuit 1 is disconnected. It can be observed from this that the MIMO system can still ensure full power output even when the transmission circuit is disconnected, which improves the operational reliability of the power transmission system.

5. Simulation and Physical Experiment Verification

5.1. Simulation Verification

According to the resonant compensation parameter configuration method in Section 3.2, the simulation parameters of the circuit where the U-shaped, E-shaped, and UE-shaped magnetic coupling structures are located are presented in

Table 1. Simulation parameters of U-shaped, E-shaped, and UE-shaped magnetic coupling structures.

	N	L (mH)	Meq (mH)	Cp (nF)	Cs (nF)
U	60	3.57	0.68	70.99	70.99
E (coil p1)	30	1.20	0.31	77.90	167.96
E (coil p2)	30	1.36	0.35	-	160.13
UE (coil p1)	20	0.65	0.20	80.89	278.99
UE (coil p2)	20	0.73	0.22	-	227.76
UE (coil p3)	20	0.78	0.23	-	226.67

Note: The primary coil groups of the E-shaped magnetic coupling structure are coils p1 and p2, and the three groups of coils on the primary side of the UE-shaped magnetic coupling structure are coils p1, p2, and p3.

. As presented in Table 1, with the increase in the number of coil layers of the proposed U-, E-, and UE-shaped magnetic coupling structures, the number of coil turns of each structure gradually decreases, and the self-inductance of the coil and mutual inductance between the coils decrease. To compare the output power levels of the U-shaped, E-shaped, and UE-shaped magnetic coupling structures at different frequencies, the output power, transmission efficiency, and failure analysis were simulated.

5.1.1. Analysis of Output Power and Transmission Efficiency

The output power curve obtained by simulation calculation is illustrated in Figure 7.

The power peaks of the three curves are illustrated in Figure 7. It can be observed that under the condition of the AC power supply of 100 V, load of 60 $\mathsf{\Omega }$, and resonant frequency of 10 kHz, the output power of the UE-shaped magnetic coupling ICPT system is 8.28 times that of the U-shaped ICPT system, in addition, the E-shaped magnetic coupling ICPT system is 4.16 times that of the U-shaped ICPT system. It can be observed that the output power of the system can be effectively increased by improving the structure of the magnetic coupling core and connection mode of the coil to meet the requirements of high-power output.

In addition to output power, transmission efficiency is also an important index for evaluating the performance of high-power wireless transmission systems. Under the same power supply and load conditions, the transmission efficiency of the ICPT system with three magnetic coupling structures is simulated and calculated, and the results are illustrated in Figure 8. It can be observed that when the resonance frequency is 10 kHz, the transmission efficiency of the circuit in which the U-shaped, E-shaped, and UE-shaped magnetic coupling structures are located decreases successively.

For the convenience of comparison, the output power and transmission efficiency of the three ICPT systems at a resonant frequency of 10 kHz are simultaneously indicated in one coordinate axis, as illustrated in Figure 9. It can be observed that compared with the SISO system, the output power of the MIMO system comprising the E-shaped magnetic coupling structure is increased by 4.16 times, while the transmission efficiency is reduced by 5.66%. The MIMO system comprising the UE-shaped magnetic coupling structure increases the output power by 8.28 times, but reduces the transmission efficiency by 10.01%. Considering that the transmission efficiency of the magnetic coupling system needs to be greater than 90%, and the peak value of the output power of the UE-shaped magnetic coupling structure at the resonance is steep, a slight change in the frequency at the resonance will lead to a significant drop in power. Therefore, considering the transmission power and efficiency, the transmission performance of the E-shaped magnetic coupling structure is better than that of the UE-shaped structure.

According to the above analysis of transmission efficiency and output power, it can be seen that with the change of magnetic coupling structure, there is a trade-off relationship between them. In the specific selection process, we should first ensure the realization of transmission efficiency, such as transmission efficiency should meet more than 90%, and then increase the number of multi-terminal coils to improve the power output. Therefore, compared with the SISO system, the magnetic coupling MIMO system composed of an E-shape structure can significantly improve the output power by optimizing the parameters. At the same time, transmission efficiency decreased only slightly.

5.1.2. Fault Simulation Analysis

The simulation results in 5.1 verify the excellent transmission performance of the MIMO system comprising the E-shaped magnetic coupling structure. In addition to the power transfer capability and efficiency, an operational reliability analysis is also necessary. Figure 10 and Figure 11 illustrate the comparison curves of the MIMO system’s output power and transmission efficiency, and the normal operating state when the secondary side coils of the MIMO system are faulty and disconnected. It can be observed that the output power before and after the fault is unchanged when running at 10 kHz, and the reduction value of the transmission efficiency is less than 3%, which has little impact on the circuit.

5.2. Physical Experiment

To verify the proposed method, an experimental platform for the SISO and MIMO systems was built, including:

• A U-shaped and E-shaped magnetic coupling structure scaled down by the medical CT machine equipment at a ratio of 10:1, as illustrated in Figure 12. To reduce the eddy current loss inside the iron core, the method of superimposing the ferrite pieces is adopted;
• Two primary side coils and two secondary side coils;
• A frequency adjustment range of 1–120 kHz high-frequency power supply;
• Resonance compensation capacitors;
• Oscilloscope;
• Protection resistor and load resistors.

The display of the experimental platform is illustrated in Figure 13. Figure 13a illustrates the SISO system. To ensure that the total number of turns of the coil is the same as that of the MIMO system, the two coils on the primary and secondary sides are connected in series in the same direction. Figure 13b illustrates the MIMO system, whose circuit is connected by the equivalent circuit illustrated in Figure 6. The two coils on the primary side are connected in series in the same direction, and the two coils on the secondary side are connected to the load. The experimental parameters of the SISO and MIMO systems are presented in

Table 2. SISO system prototype parameters.

Symbol	Value	Symbol	Value
$U_S$	100 V	$C_p$	0.13 μF
$L_p$	1.96 mH	$C_s$	0.11 μF
$L_s$	2.27 mH	$R_p$	0.13 Ω
$R_d$	10 Ω	$R_s$	0.13 Ω
$N$	60	$R_{pro}$	5 Ω
$d$	10 mm	-	-

Note: $R_{pro}$ is the protection resistor and $d$ is the air-gap between primary side and secondary side.

and

Table 3. MIMO system prototype parameters.

Symbol	Value	Symbol	Value
$U_S$	100 V	$C_{s1}$	0.32 μF
$L_{p1}$	0.69 mH	$C_{s2}$	0.27 μF
$L_{p2}$	0.78 mH	$R_{p1}$	0.06 Ω
$L_{s1}$	0.69 mH	$R_{p2}$	0.07 Ω
$L_{s2}$	0.78 mH	$R_{s1}$	0.06 Ω
$C_p$	0.17 μF	$R_{s2}$	0.07 Ω
$M_{eq1}$	0.28 mH	$N$	30
$M_{eq2}$	0.34 mH	$R_{d1}$	20 Ω
$M_{s1s2}$	0.12 mH	$R_{d2}$	20 Ω
$R_{pro}$	5 Ω	$d$	10 mm

.

5.3. Experimental Results

When the frequency is 10 kHz, the waveforms of the SISO and MIMO systems are illustrated in Figure 14. The intersections of the waveforms of each graph are marked with circles, and the right side is a zoomed-in graph. It can be observed from the figure that when the frequency is 10 kHz, the phase difference between the power supply voltage and output current of the SISO and MIMO systems is zero. That is, both are in a resonant state.

The experimental results of the output power of the SISO and MIMO systems with frequency are illustrated in Figure 15.

The resonance frequency is 10 kHz, output power of the SISO system is 106.79 W, and transmission efficiency is 94.6%. The output power of the MIMO system is 232.98 W. The transmission efficiency is 92.2%. It can be observed from the comparison experiment that the output power of the MIMO system is 2.18 times that of the SISO system under the same power supply and physical size of the magnetic coupling structure.

To verify the high reliability of the MIMO system, the coil of the secondary-side circuit 1 is disconnected. Because the experimental circuit is connected according to the equivalent circuit in Figure 6, the load will no longer be powered by two sets of power supplies after the secondary side coil is disconnected, and the equivalent load becomes 1/2 of the original.

The output power during the fault and regular operation with different loads is presented in

Table 4. Output power of different loads in the normal operating state and after secondary side coil failure.

	$10 \mathbf{\Omega }$	$20 \mathbf{\Omega }$	$30 \mathbf{\Omega }$	$40 \mathbf{\Omega }$	$50 \mathbf{\Omega }$	$60 \mathbf{\Omega }$	$70 \mathbf{\Omega }$
Normal operating state (W)	235.47	494.03	718.28	929.78	1129.4	1317.9	1495.9
Secondary fault state (W)	232.98	491.08	715.73	927.63	1127.6	1316.3	1494.5

. It can be observed that the output power fluctuates within 1% before and after the fault. Therefore, when the secondary side coil is disconnected, the output power of the secondary side of the MIMO supports each other such that the output power is unchanged.

6. Conclusions

To improve the power transmission capability of the ICPT system in high-power applications and improve the reliability of the system, the following conclusions were obtained through theoretical analysis, simulation verification, and physical experiment verification in this study:

• Based on the conventional SISO system with a U-shaped magnetic coupling structure, this paper proposed a MIMO system that comprised E-shaped and UE-shaped magnetic coupling structures with the same appearance size. By analysing the magnetic circuit, magnetic flux density, and coil of the magnetic coupling structure, it was noted that mutual coupling affected the magnetic field. It is concluded that the same directional connection of the coils of the E-shaped or UE-shaped magnetic structure has a strengthening effect on the secondary-side coupling.
• A MIMO system circuit was established, and a parameter configuration method for resonance compensation was proposed. The three-dimensional simulation software COMSOL was used to analyse the output power and transmission efficiency, respectively, and the fault analysis of the secondary side loop was performed. It is concluded that the power transmission performance of the E-shaped magnetic coupling structure is the best.
• An experimental platform of a 1 kW SISO system and MIMO system was built in the laboratory. Comparative experiments verified that under the same power supply and load, the power transmission capacity of the MIMO system was 2.18 times that of the SISO system, and the transmission efficiency was 92.2 %. Moreover, when the secondary side loop failed, the output power of the coil played the role of mutual support. The output power was unchanged, which verifies the reliability of the MIMO system.

Therefore, the MIMO system proposed in this study significantly improves the output power. In addition, the design improves the robustness and reliability of the system in parallel, can adapt to a long-term complex working environment, prolong the service life of the WPT system, and make the system have a vital redundancy feature.